SOLUTION: Company A charges a fee of 3$ plus $0.60 per page. Company B charges $0.75 per page. How many pages does the book need for company A to cost less than company B? I completely

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Company A charges a fee of 3$ plus $0.60 per page. Company B charges $0.75 per page. How many pages does the book need for company A to cost less than company B? I completely       Log On


   

Question 1124077: Company A charges a fee of 3$ plus $0.60 per page. Company B charges $0.75 per page. How many pages does the book need for company A to cost less than company B?
I completely forgot how to do this since this is a review from last year, please reply asap with steps including because I want to understand the process.
Found 3 solutions by josgarithmetic, josmiceli, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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Company A charges a fee of 3$ plus $0.60 per page. Company B charges $0.75 per page.
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x, number of pages

Company A
0.6x%2B3

Company B
0.75x


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How many pages does the book need for company A to cost less than company B?
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0.6x%2B3%3C0.75x

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is two straight line equations, and the
Intersection is the point where the costs of
A and B are the same
Let +C+ = cost and plot it on the vertical axis
Let +p+ = the number of pages plotted on horizontal axis
———————-
Company A:
(1) +C+=+.6p+%2B+3+
Company B:
(2) +C+=+.75p+
———————————
Make the costs the same:
+.75p+=+.6p+%2B+3+
+.15p+=+3+
+p+=+20+
A will cost less that B if there is 1 less page. Fractions
Of a page are probably not allowed, so 19 pages
Will make A cost less than B
Here’s the plots:
+graph%28+400%2C400%2C-10%2C30%2C-10%2C+20%2C+.6x+%2B+3%2C+.75x+%29+

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Company A charges a fee of 3$ plus $0.60 per page. Company B charges $0.75 per page. How many pages does the book need for company A to cost less than company B?
I completely forgot how to do this since this is a review from last year, please reply asap with steps including because I want to understand the process.
Let the number of pages be P

Then for company A, we get cost of: .6P + 3

For Company B, we get cost of .75P

Since Company A needs to cost less than Company B, we have the following INEQUALITY: .6P + 3 < .75P

.6P - .75P < - 3

- .15P < - 3

Number of pages for Company A to cost less than Company B:  <===== INEQUALITY sign changes when dividing by a NEGATIVE value.  

P being greater than 20 means that the number of pages is: highlight_green%2821%29